Prompt and non-prompt J/$\psi$ production and nuclear modification at mid-rapidity in p-Pb collisions at ${\bf \sqrt{{\it s}_{\text{NN}}}= 5.02}$ TeV

A measurement of beauty hadron production at mid-rapidity in proton-lead collisions at a nucleon-nucleon centre-of-mass energy $\sqrt{s_{\rm NN}}=5.02$ TeV is presented. The semi-inclusive decay channel of beauty hadrons into J/$\psi$ is considered, where the J/$\psi$ mesons are reconstructed in the dielectron decay channel at mid-rapidity down to transverse momenta of 1.3 GeV/$c$. The ${\rm {b\overline{b}}}$ production cross section at mid-rapidity, ${\rm d}\sigma_{\rm {b\overline{b}}}/{\rm d} y$, and the total cross section extrapolated over full phase space, $\sigma_{\rm {b\overline{b}}}$, are obtained. This measurement is combined with results on inclusive J/$\psi$ production to determine the prompt J/$\psi$ cross sections. The results in p-Pb collisions are then scaled to expectations from pp collisions at the same centre-of-mass energy to derive the nuclear modification factor $R_{\rm pPb}$, and compared to models to study possible nuclear modifications of the production induced by cold nuclear matter effects. $R_{\rm pPb}$ is found to be smaller than unity at low $p_{\rm T}$ for both J/$\psi$ coming from beauty hadron decays and prompt J/$\psi$.


Introduction
In high-energy hadronic collisions the production of beauty-flavoured hadrons, referred to as b-hadrons (h b ) in the following, represents a challenging testing ground for models based on quantum chromodynamics (QCD).
In proton-proton (pp) collisions the production cross sections can be computed with a factorisation approach [1,2], as a convolution of the parton distribution functions (PDFs) of the incoming protons, the partonic hard-scattering cross sections, and the fragmentation functions.
In ultra-relativistic heavy-ion collisions, where the formation of a high-density colour-deconfined medium, the Quark-Gluon Plasma (QGP), is expected [3,4], heavy quarks are considered as prime probes of the properties of the medium created in the collision.Indeed, they are produced in scattering processes with large momentum transfer in the first stage of the collision and traverse the medium interacting with its constituents, thus experiencing its full evolution.Modifications in the production of b-hadrons with respect to expectations from an incoherent superposition of elementary pp collisions can reveal the properties of the medium.However, other effects, which are not related to the presence of a QGP, the so called Cold Nuclear Matter (CNM) effects, can modify b-hadron production in heavy-ion collisions.In the initial state, the nuclear environment affects the free nucleon PDFs, which are modified depending on the parton fractional momentum x B , the four-momentum transfer squared and the atomic mass number A, as it was first observed by the European Muon Collaboration [5].At the Large Hadron Collider (LHC) energies, the most relevant effects are parton-density shadowing or gluon saturation, which can be described using modified parton distribution functions in the nucleus [6] or using the Color Glass Condensate (CGC) effective theory [7,8].Partons can also lose energy in the early stages of the collision via initial-state radiation, thus modifying the centre-of-mass energy of the partonic system [9], or experience transverse momentum broadening due to multiple soft collisions before the bb pair is produced [10][11][12].
Measurements in proton-nucleus (p-A) collisions and their comparison to pp results provide a tool to constrain the CNM effects.To quantify these effects, the nuclear modification factor can be defined as the production cross section in p-A collisions (σ pA ) divided by that in pp collisions (σ pp ) scaled by the atomic mass number A where y is the rapidity of the measured hadron in the nucleon-nucleon centre-of-mass frame, and p T its transverse momentum.In the absence of nuclear effects R pA is expected to equal unity.
Cross sections for beauty production in proton-nucleus collisions have been measured at fixed target experiments with beam energies of 800 and 920 GeV [13][14][15], corresponding to nucleon-nucleon centreof-mass energies up to √ s NN = 41.6 GeV.Measurements at the LHC in p-Pb collisions are sensitive to a previously unexplored parton kinematic domain of the colliding nucleons, in particular to small values of the gluonic content of the nucleon x B .For instance, in the perturbative QCD leading order process gg → bb the threshold production of a bb pair at y = 0 and y = 3 in p-Pb collisions at √ s NN = 5.02 TeV is obtained, respectively, for x B ≈ 10 −3 and 10 −4 [16].The LHCb experiment has measured beauty production at backward and forward rapidity [17,18], where "forward" and "backward" are defined relative to the direction of the proton, reporting R pPb = 0.83 ± 0.08 at forward rapidity (1.5 < y < 4) and R pPb = 0.98 ± 0.12 at backward rapidity (−5 < y < −2.5) in p-Pb collisions at √ s NN = 5.02 TeV.Results at mid-rapidity have been reported from the ATLAS and CMS experiments, based on either exclusively reconstructed beauty mesons [19], or semi-inclusive decays h b → J/ψ + X [20][21][22] or beauty jets [23].These measurements however do not cover, at mid-rapidity, the low p T region where the nuclear effects are expected to be the largest and the bulk of the total b-hadron production is concentrated.ALICE has measured beauty production in p-Pb collisions at √ s NN = 5.02 TeV through the semi-leptonic decay channel, h b → e + X, down to a transverse momentum of the decay electron of 1 GeV/c, finding R pPb

Data sample and analysis
The ALICE apparatus [28,29] consists of a central barrel, covering the pseudorapidity region |η| < 0.9, a muon spectrometer with −4 < η < −2.5 coverage, and forward and backward detectors employed for triggering, background rejection and event characterisation.The central-barrel detectors that have been used to reconstruct J/ψ → e + e − decays are the Inner Tracking System (ITS) and the Time Projection Chamber (TPC).They are located inside a large solenoidal magnet with a field strength of 0.5 T. The ITS [30] consists of six layers of silicon detectors surrounding the beam pipe at radial positions between 3.9 and 43.0 cm.Its two innermost layers are composed of Silicon Pixel Detectors (SPD), which provide the spatial resolution to separate on a statistical basis the prompt and non-prompt J/ψ components.The active volume of the TPC [31] covers the range along the beam direction |z| < 250 cm relative to the nominal interaction point and extends in radial direction from 85 cm to 247 cm.It is the main tracking device in the central barrel and, in addition, it is used for particle identification via the measurement of the specific energy loss (dE/dx) in the detector gas.This analysis is based on the data sample collected during the 2013 LHC p-Pb run, corresponding to an integrated luminosity L int = 51.4 ± 1.9 µb −1 .The events were selected using a minimum-bias trigger provided by the V0 detector [32], a system of two arrays of 32 scintillator tiles each covering the full azimuth within 2.8 < η < 5.1 (V0A) and −3.7 < η < −1.7 (V0C).The trigger required at least one hit in both the V0A and the V0C scintillator arrays, and the non-single-diffractive p-Pb collisions were selected with an efficiency higher than > 99%.A radiator-quartz detector, the T0 system [33], provided a measurement of the time of the collisions.The V0 and T0 time resolutions allowed discrimination of beam-beam interactions from background events in the interaction region.Further background suppression was applied in the offline analysis using temporal information from the neutron Zero Degree Calorimeters [34,35].
The reconstruction of the J/ψ in the e + e − decay channel is described in detail in reference [25].The tracks were reconstructed with the ITS and TPC detectors and required to have p T > 1.0 GeV/c and |η| < 0.9, a minimum number of 70 TPC clusters per track (out of a maximum of 159), a χ 2 per space point of the track fit lower than 4, and at least one hit in the SPD.Electrons and positrons selection was based on the dE/dx values measured in the TPC: the dE/dx signal was required to be compatible Prompt and non-prompt J/ψ production in p-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration with the mean electron energy loss within ±3σ , where σ denotes the resolution of the dE/dx measurement.Furthermore, tracks consistent with the pion and proton assumptions were rejected.Electrons and positrons that, when paired, were found compatible with being result of photon conversions were also removed, in order to reduce the combinatorial background.It was verified, using a Monte Carlo simulation, that this procedure does not affect the J/ψ signal.J/ψ candidates were then obtained by pairing the selected positron and electron candidates in the same event and requiring the J/ψ rapidity to be within −1.37 < y < 0.43 (i.e.|y lab | < 0.9 in the laboratory system).The condition that at least one of the two decay tracks has a hit in the innermost SPD layer was also required in order to enhance the resolution of the J/ψ decay vertices.
The measurement of the fraction of the J/ψ yield originating from b-hadron decays, f b , relies on the discrimination of J/ψ mesons produced at a distance from the primary p-Pb collision vertex.The pseudoproper decay length variable x is defined as where L is the vector pointing from the primary vertex to the J/ψ decay vertex and m J/ψ is the J/ψ pole mass value [36].The x resolution is about 150 µm (60 µm) for J/ψ of p T = 1.5 GeV/c (5 GeV/c).This allows to determine the fraction of J/ψ from the decay of b-hadrons for events with J/ψ p T greater than 1.3 GeV/c.The same approach used in similar analyses for the pp [37] and Pb-Pb [38] colliding systems is adopted here.It is based on an unbinned two-dimensional fit, which is performed by minimising the opposite of the logarithm of the likelihood function L (m e + e − , x), where N is the number of e + e − pairs in the invariant mass range 2.2 < m e + e − < 4.0 GeV/c 2 , F Sig (x) and F Bkg (x) are Probability Density Functions (PrDFs) describing the pseudoproper decay length distribution for signal (prompt and non-prompt J/ψ ) and background candidates, respectively.Similarly, M Sig (m e + e − ) and M Bkg (m e + e − ) are the PrDFs describing the e + e − invariant mass distributions for the two components.The signal fraction f Sig is defined as the ratio of the number of signal candidates over the sum of signal and background candidates.The fraction of non-prompt J/ψ enters into F Sig (x) as: where F prompt (x) and F b (x) are the PrDFs for prompt and non-prompt J/ψ , respectively, and f b is the uncorrected fraction of J/ψ coming from b-hadron decays.A small correction due to the different acceptance times efficiency, averaged over p T in a given p T interval ( A × ε ) for prompt and non-prompt J/ψ is necessary to obtain f b from f b : The difference in A × ε originates from the different p T distributions of prompt and non-prompt J/ψ and the assumption on their spin alignment, as discussed later.The different components entering into the determination of f b are described in detail in [37,38].An improved procedure was introduced in this analysis to determine the resolution function, R(x), which describes the accuracy by which x can be reconstructed and is the key ingredient of F prompt (x), F b (x) and F Bkg (x).R(x) was determined using Monte Carlo simulations and considering the x distributions of prompt J/ψ reconstructed with the same procedure and selection criteria as for data.It was parameterised with a double-Gaussian core and a power function (∝ |x| −λ ) for the tails [37].A tuning of the Monte Carlo simulation was applied to minimise the residual discrepancy between data and simulation for the distribution of the impact parameter of single charged tracks.The systematic uncertainty related to the incomplete knowledge of R(x) was thus reduced, as discussed later.
Prompt and non-prompt J/ψ production in p-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration 3 GeV/c with superimposed projections of the maximum likelihood fit.The latter distribution is limited to the J/ψ candidates under the mass peak, i.e. for 2.92 < m e + e − < 3.16 GeV/c 2 , for display purposes only.The χ 2 values of these projections are also reported for both distributions.
In Fig. 1 the distributions of the invariant mass and the pseudoproper decay length for opposite-sign electron pairs with p T > 1.3 GeV/c are shown with superimposed projections of the likelihood fit result.Although the J/ψ signal yield is not large, amounting to 360 counts for p T > 1.3 GeV/c, the data sample could be divided into three p T intervals (1.3-3.0,3.0-5.0and 5.0-10 GeV/c), and the fraction f b was evaluated in each interval with the same technique.At low p T there are more candidates, but the resolution is worse and the signal over background, S/B, is smaller (i.e.f Sig is smaller).At higher p T the number of candidates is smaller, but the resolution improves and the background becomes minor.In Fig. 2 the distributions of the invariant mass and of the pseudoproper decay length are shown in different p T intervals with superimposed projections of the best fit functions.The values of the fraction of non-prompt J/ψ are evaluated with Eq. 4 assuming unpolarised prompt J/ψ .The relative variations of f b expected in extreme scenarios for the polarisation of prompt J/ψ were studied in [37].For non-prompt J/ψ , a small polarisation is obtained using EvtGen [39] as the result of the averaging effect caused by the admixture of various exclusive b-hadron decay channels.The extreme assumption of a null polarisation also for non-prompt J/ψ results in a relative decrease of f b by only 1% at p T of about 10 GeV/c and 4% at lower p T (1.3-3.0GeV/c).The uncertainties related to the polarisation of prompt and non-prompt J/ψ are not further propagated to the results, this choice being motivated by the small degree of polarisation measured in pp collisions at √ s = 7 TeV [40][41][42].
The p T and y distributions used as input to the Monte Carlo simulations assume for prompt J/ψ the shape from next-to-leading order (NLO) Color Evaporation Model (CEM) calculations [43][44][45], and take into account nuclear effects according to the EPS09 parameterisation [46].For the non-prompt J/ψ , b-hadrons were generated using PYTHIA 6.4.21 [47] with the Perugia-0 tune [48] and the nuclear shadowing provided by the EPS09 parameterisation was also introduced.In both cases the signal events were injected into p-Pb collisions simulated with HIJING [49], and a full simulation of the detector response was performed adopting GEANT3 [50] as particle transport code.The particle decay was simulated with the EvtGen package [39], using the PHOTOS model [51] to properly describe the J/ψ radiative decay channel (J/ψ → e + e − γ).The same reconstruction procedure and selection criteria were applied to simulated events as to real data.
The systematic uncertainties in the determination of f b arise mainly from uncertainties on the resolution function, and the x and m e + e − PrDFs for background pairs, prompt and non-prompt J/ψ .They were estimated by propagating the residual discrepancy between Monte Carlo simulations and data, varying the functional forms assumed for the different PrDFs, and repeating the fitting procedure with similar approaches as those described in [37,38].The uncertainty on the shape of the p T distributions in the Monte Carlo simulations introduces also a systematic uncertainty in the determination of f b .In fact, the Monte Carlo simulations have been used to determine p T -dependent quantities that were averaged over finite-size p T intervals as, e.g.A × ε , and the result of the average depends on the p T shape.Different assumptions for the p T distributions were considered, resulting in variations for the average p T of ∼ 15% for both prompt and non-prompt components in the p T integrated sample.These include cases without nuclear shadowing, a parameterisation of the non-prompt component from perturbative QCD calculations at fixed order with next-to leading-log re-summation (FONLL) [52] and a parameterisation of the prompt component with the phenomenological function defined in [53].Due to the weak p T dependence of A × ε, this uncertainty is found to be significant only for the p T -integrated case 1 .Table 1 summarises the systematic uncertainties for the p T -integrated result (p T > 1.3 GeV/c) and the three p T intervals.
The value of f b in pp collisions at √ s = 5.02 TeV, f pp b , is needed to compute the R pPb for prompt and non-prompt J/ψ mesons, for prompt J/ψ and where R incl.J/ψ pPb is the nuclear modification factor for inclusive J/ψ measured in [25].5.02 TeV.It is based on experimental data (shown in Fig. 3) from CDF in pp collisions [57] at lower centre-of-mass energy (1.96 TeV) and from ALICE [37], ATLAS [58] and CMS [59] in pp collisions at higher energy (7 TeV).The value for p T > 1.  2: Fraction of non-prompt J/ψ in pp collisions at √ s = 5.02 TeV for different p T ranges, as determined with the procedure of interpolation described in [38], and that measured in p-Pb collisions in this analysis.For the latter, the first uncertainty is statistical, the second one is systematical.The upper limit at 95% confidence level is given for the interval 1.3 < p T < 3 GeV/c.

Results
The fraction of J/ψ yield originating from decays of b-hadrons in the experimentally accessible kinematic range, p t > 1.3 GeV/c and −1.37 < y < 0.43, which is referred to as "visible region" in the following, is found to be f b = 0.105 ± 0.038 (stat.)± 0.012 (syst.).
The results in the different p T intervals are reported in Tab. 2. In the interval 1.3 < p T < 3 GeV/c the minimum of Eq. 2, which is obtained for f b = 0.05, is broad and it was not possible to define 1σ symmetric uncertainty bounds within the physical region f b > 0. Therefore an upper limit at the 95% confidence level was derived assuming normally distributed uncertainties.Figure 3 shows the fraction of non-prompt J/ψ as a function of p T compared to the results of ATLAS [20] covering the high p T region (p T > 8 GeV/c) in a similar rapidity range (−1.94 < y < 0).In the figure, the ALICE data symbols are placed horizontally at the average value of the p T distribution of each interval.The average was computed using the Monte Carlo simulations, which are described in the previous section, weighted by the measured f b .In Fig. 3 the results of CDF [57] for pp collisions at √ s = 1.96TeV and of ALICE [37], ATLAS [60] and CMS [59] experiments in pp collisions at either √ s = 7 or √ s = 8 TeV are also shown.
By combining the measurement of inclusive J/ψ cross sections [25] with the f b determinations, the  [20] in the same colliding system and results of ALICE [37], ATLAS [60] and CMS [59] in pp collisions at either √ s = 7 TeV or √ s = 8 TeV.Results from CDF [57] in pp collisions at √ s = 1.96TeV are also shown.The ALICE data symbols are placed horizontally at the average value of the p T distribution of each interval (see text for details).For all experiments, the vertical error bars represent the quadratic sum of the statistical and systematic errors.In the interval 1.3 < p T < 3 GeV/c the upper limit at the 95% confidence level is shown, as discussed in the text.
prompt and non-prompt J/ψ production cross sections were obtained as follows: In the visible region the following value is derived for the non-prompt component: The visible cross section of non-prompt J/ψ production was extrapolated down to p T = 0 using FONLL calculations [52] with CTEQ6.6 PDFs [61] and nuclear modification of the parton distribution functions (nPDFs) from the EPPS16 parameterisation [54].The fragmentation of b-quarks into hadrons was performed using PYTHIA 6.4.21 [47] with the Perugia-0 tune [48].The extrapolation factor, which is equal to 1.22 +0.02 −0.04 , was computed as the ratio of the cross section for p J/ψ T > 0 and −1.37 < y < 0.43 to that in the visible region.The uncertainty on the extrapolation factor was determined by combining the FONLL, CTEQ6.6 and EPPS16 uncertainties.The FONLL uncertainties have been evaluated by varying the factorisation and renormalisation scales, µ F and µ R , independently in the ranges 0.5 The b-quark mass was varied within 4.5 < m b < 5.0 GeV/c 2 .The CTEQ6.6 and EPPS16 uncertainties were propagated according to the Hessian prescription of the authors of these parameterisations (Eq.53 of reference [54]).The extrapolated p T -integrated non-prompt J/ψ cross section per unit of rapidity is obtained by dividing by the rapidity range ∆y = 1.8: dσ J/ψ from h b dy = 93 ± 35 (stat.)± 13 (syst.)+2 −3 (extr.)µb.
In the left panel of Fig. 4 this measurement is plotted together with the LHCb [17] [20].The error bars represent the statistical uncertainties, while the systematic uncertainties are shown as boxes.In the right panel, the upper limit at the 95% confidence level is shown with an arrow for the interval 1.3 < p T < 3 GeV/c.The systematic uncertainty on the extrapolation to p T = 0 (left panel only) is indicated by the filled red box.Results from FONLL computations [52] with EPPS16 [54] nuclear modification of the CTEQ6.6PDFs [61] are shown superimposed, including the total theoretical uncertainty (empty band/boxes) and the EPPS16 contribution (coloured band/boxes).
show the total theoretical uncertainties, while the coloured band corresponds to the contribution from the EPPS16 uncertainties.The cross section was also computed, according to Eq. 6, in the three p T intervals and compared to the ATLAS measurements [20] for −1.94 < y < 0 and p T > 8 GeV/c (right panel of Fig. 4).The ALICE measurement, which covers the low p T region at mid-rapidity, is thus complementary to the data of the other LHC experiments.The total theoretical uncertainties on the production cross section, which are dominated by those of the b-quark mass and the QCD factorisation and renormalisation scales, are larger than the experimental uncertainties, preventing to draw conclusions on the presence of nuclear effects for this observable.
The dominant uncertainties of the theoretical predictions cancel out when considering the nuclear modification factor R pPb , which was determined experimentally according to Eq. 5. Figure 5 shows the R pPb of non-prompt J/ψ for p T > 0 as compared to the LHCb measurements at backward and forward rapidity [17] (left panel) and as a function of p T as compared to CMS results [21] (right panel).The results are also compared to the FONLL pQCD calculations with EPPS16 nPDFs described previously.The central value of an alternative parameterisation of the nuclear PDF, nDSgLO [62], is also shown for comparison in the left-hand plot.The p T -integrated R pPb , which is R pPb = 0.54 ± 0.20(stat.)± 0.13(syst.)+0.01 −0.02 (extr.), is measured to be smaller than unity with a significance of 2.3/3.5/1.9 σ (statistical/systematic/combined).The p T dependence suggests that the suppression of the production originates at low p T .The bb production cross section at mid-rapidity was obtained as In the left hand panel, the results from the LHCb experiment are taken from [17] and the systematic uncertainty on the extrapolation to p T = 0 for the ALICE data point is depicted by the filled red box.In the right hand plot, the results from the CMS experiment are taken from [21] and the arrow shows the upper limit at 95% confidence level for the interval 1.3 < p T < 3 GeV/c.The nuclear modification factors as expected from the EPPS16 [54] and the nDSg [62]  The total bb production cross section was computed similarly by extrapolating the visible cross section to the full phase space as where α 4π is the ratio between the yield of J/ψ mesons (from the decay of b-hadrons) in the full phase space and the yield in the visible region, and the factor 2 takes into account that b-hadrons originate from both b and b quarks.The extrapolation factor α 4π was also computed based on FONLL pQCD calculations with EPPS16 nPDFs, with the b-quark fragmentation performed using PYTHIA 6.4.21 with the Perugia-0 tune, and found to be α 4π = 4.1 ± 0.2.The resulting cross section is σ (pPb → bb + X) = 25 ± 9(stat.)± 4(syst.)± 1(extr.)mb (ALICE only).
The ALICE measurement is shown in Fig. 6 along with the other existing measurements in p-A collisions, which were obtained in fixed-target experiments [13][14][15] at lower √ s NN .The experimental results are compared to the FONLL calculations using the EPPS16 nPDFs.
The combination with the LHCb measurements [17] allows us to extract the total bb cross section with a significant reduction of the uncertainty.The factor α 4π , which is computed as the ratio of the yield in full phase space over that covered by ALICE and LHCb, reduces to 1.60 +0.02 −0.03 and the total cross section becomes σ (pPb → bb + X) = 29 ± 4(stat.)± 3(syst.)± 1(extr.)mb (ALICE and LHCb).Fig. 6: Beauty production cross section in p-A collisions as a function of √ s NN as measured by ALICE and at fixed-target experiments (E789 [13], E771 [14] and HERA-B [15]).The FONLL calculations with EPPS16 nuclear modification to the PDFs are superimposed in orange.The full lines show the total theoretical uncertainty, while the coloured band corresponds to the contribution from the EPPS16 uncertainties.
The p T differential cross section was derived using Eq. 6.The numerical values are reported in Tab.The nuclear modification factor for prompt J/ψ was computed using Eq. 5.With respect to the results discussed in [25], where the inclusive J/ψ production in p-Pb collisions at √ s NN = 5.02 TeV was presented, a more direct comparison with model predictions can now be performed.Figure 7 shows the R pPb of prompt J/ψ compared to predictions from various models.The results indicate that the suppression observed at mid-rapidity is a low p T effect, as also argued for non-prompt J/ψ .One calculation (Vogt [45,66]) is based on the NLO CEM for the prompt J/ψ production and the EPS09 NLO shadowing parameterisation.The theoretical uncertainties arise from those in EPS09 and from the values of the charm quark mass and of the renormalisation and factorisation scales.A second calculation (Arleo et al. [67]) is based on a parameterisation of experimental results on prompt J/ψ production in pp collisions, including the effects of coherent energy loss in the cold nuclear medium with or without introducing shadowing effects according to the EPS09 NLO parameterisation.The model of Ferreiro et al. [68] employs the EPS09 Leading Order (LO) nPDF with or without effects from the interaction with a nuclear medium.The last set of models are based on different implementations of the CGC effective theory, which assumes a regime of gluon saturation (see [7,8] for reviews), by using either the CEM for the  [17].The box around R pPb = 1 in the right panel shows the size of the correlated relative uncertainty.Results from various models [45, 66-70, 72, 73] are also shown, see text for details.
prompt J/ψ production (Fujii et al. [69] and Ducloué et al. [70]) or the non-relativistic QCD (NRQCD) factorisation approach [71] (Ma et al. [72]).The results suggest the presence of nuclear effects in the low p T region, but the present uncertainties do not allow us to discriminate among the different models.

Summary
The production of b-hadrons in p-Pb collisions at √ s NN = 5.02 TeV through the inclusive decay channel h b → J/ψ + X has been measured at mid-rapidity and down to J/ψ p T of 1.3 GeV/c.The mid-rapidity dσ bb /dy and the total bb cross section, σ bb , were derived.The nuclear modification factor of beauty production at mid-rapidity, integrated over p T , is R pPb = 0.54 ± 0.20(stat.)± 0.13(syst.)+0.01 −0.02 (extr.)and compatible within uncertainties to expectations from the EPPS16 parameterisation of the nuclear modification to the PDFs.The production cross section of prompt J/ψ was obtained by subtracting the non-prompt component from a previous measurement of the inclusive J/ψ production.The nuclear modification factor of prompt J/ψ indicates a reduced production of low p T J/ψ , with respect to expectations from scaled pp collisions, but the present uncertainties do not allow us to discriminate among different models.

Fig. 1 :
Fig.1: Invariant mass (left panel) and pseudoproper decay length (right panel) distributions for J/ψ candidates with p T > 1.3 GeV/c with superimposed projections of the maximum likelihood fit.The latter distribution is limited to the J/ψ candidates under the mass peak, i.e. for 2.92 < m e + e − < 3.16 GeV/c 2 , for display purposes only.The χ 2 values of these projections are also reported for both distributions.

Fig. 2 :
Fig.2: Invariant mass (left panels) and pseudoproper decay length (right panels) distributions in different p T intervals with superimposed projections of the maximum likelihood fit.The x distributions are limited to the J/ψ candidates under the mass peak.The χ 2 values of these projections are also reported for all distributions.

Fig. 3 :
Fig.3: Fraction of J/ψ from the decay of b-hadrons at mid-rapidity as a function of the p T of J/ψ in p-Pb collisions at √ s NN = 5.02 TeV compared with results from ATLAS[20] in the same colliding system and results of ALICE[37], ATLAS[60] and CMS[59] in pp collisions at either √ s = 7 TeV or √ s = 8 TeV.Results from CDF[57] in pp collisions at √ s = 1.96TeV are also shown.The ALICE data symbols are placed horizontally at the average value of the p T distribution of each interval (see text for details).For all experiments, the vertical error bars represent the quadratic sum of the statistical and systematic errors.In the interval 1.3 < p T < 3 GeV/c the upper limit at the 95% confidence level is shown, as discussed in the text.

Fig. 4 :
Fig.4: dσ J/ψ from h b /dy as a function of y (left panel) compared to results obtained in the forward and backward rapidity regions by LHCb[17] and d 2 σ J/ψ from h b /dy dp T as a function of p T (right panel) compared to ATLAS results[20].The error bars represent the statistical uncertainties, while the systematic uncertainties are shown as boxes.In the right panel, the upper limit at the 95% confidence level is shown with an arrow for the interval 1.3 < p T < 3 GeV/c.The systematic uncertainty on the extrapolation to p T = 0 (left panel only) is indicated by the filled red box.Results from FONLL computations[52] with EPPS16[54] nuclear modification of the CTEQ6.6PDFs[61] are shown superimposed, including the total theoretical uncertainty (empty band/boxes) and the EPPS16 contribution (coloured band/boxes).

Fig. 5 :
Fig.5: The nuclear modification factor R pPb of non-prompt J/ψ as a function of rapidity for p T > 0 (left panel) and as a function of p T at mid-rapidity (right panel).The error bars and the open boxes indicate, respectively, the statistical and systematic uncertainties.In the left hand panel, the results from the LHCb experiment are taken from[17] and the systematic uncertainty on the extrapolation to p T = 0 for the ALICE data point is depicted by the filled red box.In the right hand plot, the results from the CMS experiment are taken from[21] and the arrow shows the upper limit at 95% confidence level for the interval 1.3 < p T < 3 GeV/c.The nuclear modification factors as expected from the EPPS16[54] and the nDSg[62] (central value shown in the left panel only) parameterisations are shown superimposed.
Fig.5: The nuclear modification factor R pPb of non-prompt J/ψ as a function of rapidity for p T > 0 (left panel) and as a function of p T at mid-rapidity (right panel).The error bars and the open boxes indicate, respectively, the statistical and systematic uncertainties.In the left hand panel, the results from the LHCb experiment are taken from[17] and the systematic uncertainty on the extrapolation to p T = 0 for the ALICE data point is depicted by the filled red box.In the right hand plot, the results from the CMS experiment are taken from[21] and the arrow shows the upper limit at 95% confidence level for the interval 1.3 < p T < 3 GeV/c.The nuclear modification factors as expected from the EPPS16[54] and the nDSg[62] (central value shown in the left panel only) parameterisations are shown superimposed.
Prompt and non-prompt J/ψ production in p-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration

Fig. 7 :
Fig. 7: R pPb of prompt J/ψ versus rapidity (left panel) and as a function of p T at mid-rapidity (right panel), compared to theoretical calculations.Statistical uncertainties are represented by vertical error bars, while open boxes correspond to systematic uncertainties.Results from the LHCb experiment at backward and forward rapidity are shown in the left panel[17].The box around R pPb = 1 in the right panel shows the size of the correlated relative uncertainty.Results from various models[45, 66-70, 72, 73]  are also shown, see text for details.

Table 1 :
Systematic uncertainties (in percent) on the measurement of the fraction f b of J/ψ from the decay of b-hadrons, for different transverse momentum ranges.The symbol "-" is used to indicate a negligible contribution.
The values obtained in other p T intervals are reported in the central column of Tab. 2.

Table 3 :
The production cross section of prompt J/ψ as a function of p T in p-Pb collisions at √ s NN = 5.02 TeV measured for −1.37 < y < 0.43.The first quoted uncertainty is statistical, the second (third) is the systematical one that is correlated (uncorrelated) in p T .